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If A is a square matrix of ordern, then t(a * dj(a * dj(a * dj(A)))) =

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$t(A \cdot \operatorname{adj}(A) \cdot \operatorname{adj}(A) \cdot \operatorname{adj}(A))=t\left(A \cdot \operatorname{adj}(A)^3\right)$

$\operatorname{adj}(A)=\operatorname{det}(A) \cdot A^{-1} \Rightarrow \operatorname{adj}(A)^3=(\operatorname{det}(A))^3 \cdot A^{-3}$

$A \cdot \operatorname{adj}(A)^3=(\operatorname{det}(A))^3 \cdot A \cdot A^{-3}=(\operatorname{det}(A))^3 \cdot A^{-2}$

$t\left(A \cdot \operatorname{adj}(A)^3\right)=(\operatorname{det}(A))^3 \cdot\left(A^{-2}\right)^{T}$

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Divya Sharma

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